A generalisation of Mahler measure and its application in algebraic dynamical systems
Acta Arithmetica (1999)
- Volume: 88, Issue: 1, page 15-29
- ISSN: 0065-1036
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topManfred Einsiedler. "A generalisation of Mahler measure and its application in algebraic dynamical systems." Acta Arithmetica 88.1 (1999): 15-29. <http://eudml.org/doc/207228>.
@article{ManfredEinsiedler1999,
abstract = {We prove a generalisation of the entropy formula for certain algebraic $ℤ^d$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.},
author = {Manfred Einsiedler},
journal = {Acta Arithmetica},
keywords = {Mahler measure; topological entropy; dynamical system},
language = {eng},
number = {1},
pages = {15-29},
title = {A generalisation of Mahler measure and its application in algebraic dynamical systems},
url = {http://eudml.org/doc/207228},
volume = {88},
year = {1999},
}
TY - JOUR
AU - Manfred Einsiedler
TI - A generalisation of Mahler measure and its application in algebraic dynamical systems
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 1
SP - 15
EP - 29
AB - We prove a generalisation of the entropy formula for certain algebraic $ℤ^d$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
LA - eng
KW - Mahler measure; topological entropy; dynamical system
UR - http://eudml.org/doc/207228
ER -
References
top- [1] D. Hilbert, Gesammelte Abhandlungen, Bd. I, Springer, Berlin, 1932.
- [2] D. A. Lind, K. Schmidt and T. Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), 593-629. Zbl0774.22002
- [3] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992.
- [4] K. Schmidt, Dynamical Systems of Algebraic Origin, Birkhäuser, 1995. Zbl0833.28001
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